7. Optional extra credit: flash mob! You've accepted a summer internship at a startup that's making...

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7. Optional extra credit: flash mob! You've accepted a summer internship at a startup that's making a new flash mob app. Here's how it works: Given n people in the plane, the app will periodically convene a flash mob of size k, where k is some constant. The objective is to find a size-k subset of the n people so that the sum of the pairwise distances between those k people is as small as possible. In other words, given a set of n points, we wish to find a subset P of exactly k points that minimizes the sum p,qep d(p,q), where d(.,.) denotes the Euclidean distance. Give an O(nlogn)-time algorithm for this problem. Solution: 7. Optional extra credit: flash mob! You've accepted a summer internship at a startup that's making a new flash mob app. Here's how it works: Given n people in the plane, the app will periodically convene a flash mob of size k, where k is some constant. The objective is to find a size-k subset of the n people so that the sum of the pairwise distances between those k people is as small as possible. In other words, given a set of n points, we wish to find a subset P of exactly k points that minimizes the sum p,qep d(p,q), where d(.,.) denotes the Euclidean distance. Give an O(nlogn)-time algorithm for this problem. Solution: